Signal detection theory worksheet by hedongchenchen

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									                                                              Criterion (in Noise dist. SD units)
Noise dist.     p-value       SN dist.         p-value                        P(Hit)        P(False alarm)
            0    0.004431848               1    0.00443185                0.5 0.99976737 0.99379033
          0.1    0.005952532             1.1    0.00595253              0.75 0.99942297 0.98777553
          0.2    0.007915452             1.2    0.00791545                  1   0.9986501 0.97724987
          0.3    0.010420935             1.3    0.01042093              1.25 0.99702024 0.95994084
          0.4    0.013582969             1.4    0.01358297                1.5 0.99379033        0.9331928
          0.5       0.0175283            1.5      0.0175283             1.75 0.98777553 0.89435023
          0.6     0.02239453             1.6    0.02239453                  2 0.97724987 0.84134475
          0.7    0.028327038             1.7    0.02832704              2.25 0.95994084 0.77337265
          0.8    0.035474593             1.8    0.03547459                2.5   0.9331928 0.69146246
          0.9    0.043983596             1.9      0.0439836             2.75 0.89435023 0.59870633
            1    0.053990967               2    0.05399097                  3 0.84134475               0.5
          1.1    0.065615815             2.1    0.06561581              3.25 0.77337265 0.40129367
          1.2    0.078950158             2.2    0.07895016                3.5 0.69146246 0.30853754
          1.3    0.094049077             2.3    0.09404908              3.75 0.59870633 0.22662735
          1.4    0.110920835             2.4    0.11092083                  4            0.5 0.15865525
          1.5    0.129517596             2.5      0.1295176             4.25 0.40129367 0.10564977
          1.6    0.149727466             2.6    0.14972747                4.5 0.30853754        0.0668072
          1.7    0.171368592             2.7    0.17136859              4.75 0.22662735 0.04005916
          1.8    0.194186055             2.8    0.19418605                  5 0.15865525 0.02275013
          1.9    0.217852177             2.9    0.21785218              5.25 0.10564977 0.01222447
            2    0.241970725               3    0.24197072                5.5   0.0668072 0.00620967
          2.1     0.26608525             3.1    0.26608525              5.75 0.04005916 0.00297976
          2.2    0.289691553             3.2    0.28969155                  6 0.02275013        0.0013499
          2.3    0.312253933             3.3    0.31225393
          2.4    0.333224603             3.4      0.3332246
          2.5    0.352065327             3.5    0.35206533
          2.6     0.36827014             3.6    0.36827014
          2.7    0.381387815             3.7    0.38138782              3.5             0
          2.8    0.391042694             3.8    0.39104269              3.5          0.05
          2.9    0.396952547             3.9    0.39695255              3.5           0.1
            3     0.39894228               4    0.39894228              3.5          0.15
          3.1    0.396952547             4.1    0.39695255              3.5           0.2
          3.2    0.391042694             4.2    0.39104269              3.5          0.25
          3.3    0.381387815             4.3    0.38138782              3.5           0.3
          3.4     0.36827014             4.4    0.36827014              3.5          0.35
          3.5    0.352065327             4.5    0.35206533              3.5           0.4
          3.6    0.333224603             4.6      0.3332246             3.5          0.45
          3.7    0.312253933             4.7    0.31225393
          3.8    0.289691553             4.8    0.28969155
          3.9     0.26608525             4.9    0.26608525
            4    0.241970725               5    0.24197072
          4.1    0.217852177             5.1    0.21785218
          4.2    0.194186055             5.2    0.19418605
          4.3    0.171368592             5.3    0.17136859
          4.4    0.149727466             5.4    0.14972747
          4.5    0.129517596             5.5      0.1295176
          4.6    0.110920835             5.6    0.11092083
          4.7    0.094049077             5.7    0.09404908
          4.8    0.078950158             5.8    0.07895016
          4.9    0.065615815             5.9    0.06561581
            5    0.053990967               6    0.05399097
          5.1    0.043983596             6.1      0.0439836
          5.2    0.035474593             6.2    0.03547459
          5.3    0.028327038             6.3    0.02832704
          5.4     0.02239453             6.4    0.02239453
5.5      0.0175283   6.5    0.0175283
5.6   0.013582969    6.6   0.01358297
5.7   0.010420935    6.7   0.01042093
5.8   0.007915452    6.8   0.00791545
5.9   0.005952532    6.9   0.00595253
  6   0.004431848      7   0.00443185
d'       c
     1        0.5
     1       0.75
     1          1
     1       1.25
     1        1.5
     1       1.75
     1          2
     1       2.25
     1        2.5
     1       2.75
     1          3
     1       3.25
     1        3.5
     1       3.75
     1          4
     1       4.25
     1        4.5
     1       4.75
     1          5
     1       5.25
     1        5.5
     1       5.75
     1          6

     1
Difference between means (in sensory intensity units) =              1
                                                                                                                        Underlying probability dens

       Criterion*                    P(Hit) P(False alarm)     d'?
              3.5                     0.69           0.31

* Criterion is expressed in units of sensory intensity




                                                                         Probability
                                                                                       0                      1     2      3           4
                                                                                                                                Sensory intensity



Observed P(Hit) Observed P(False alarm)                  d'?   c?
          0.20                    0.04
          0.47                    0.16
          0.71                    0.31
          0.87                    0.60                                                               1

          0.98                    0.77

                                                                                                    0.8




                                                                                                    0.6
                                                                                           P(Hit)




                                                                                                    0.4




                                                                                                    0.2




                                                                                                     0
                                                                                                          0       0.2    0.4     0.6

                                                                                                                        P(False alarm)
Underlying probability density functions




                                                               Noise alone
                                                               Signal + noise
                                                               Criterion




               4         5       6   7    8         9
        Sensory intensity




                    ROC curve




                                         Interpolated curve
                                         Observed datapoints




         0.6       0.8       1

P(False alarm)

								
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